Question

Please answer correctly !!!!!!!!!!!! Will mark Brianliest !!!!!!!!!!!!!!!!

Answer 1

RS = 11

Explanation:

well from the mid-point theorem we have that

`\triangle PRS \sim \triangle PNQ`

by a ratio of

`1:2`

so

`(RS)/(NQ)=(1)/(2)\\\\2[(RS)/(NQ)]=2[(1)/(2)]\\\\(2RS)/(NQ)=1\\\\NQ[(2RS)/(NQ)]=NQ[1]\\\\2RS=NQ`

and now we plug in

`RS = 5x-39\\\\NQ = 4x-18`

`2[5x-39]=4x-18\\\\10x-78=4x-18\\\\10x-4x=-18+78\\\\6x=60\\\\x=10`

so the length of RS is

`RS = 5x-39\\\\RS = 5(10)-39\\\\RS=50-39\\\\RS=11`